MSK spread-spectrum receiver which allows CDMA operations

ABSTRACT

A method for demodulating a received spread-spectrum signal using a minimum-shift-keyed (MSK) receiver. Using the method, an in-phase-component signal and a quadrature-phase-component signal are generated from a received spread-spectrum signal. The in-phase-component signal and the quadrature-phase-component signal are then processed and combined in such a way as to estimate data of the received-spread-spectrum signal.

BACKGROUND OF THE INVENTION

This invention relates to spread-spectrum communications, and moreparticularly to an minimum shift keyed (MSK) receiver which can be usedin a code division multiple access (CDMA) spread-spectrum communicationsenvironment.

DESCRIPTION OF THE RELEVANT ART

Using MSK modulation is desirable because this type of modulation has aconstant envelope signal and can be used with a more efficient Class Camplifier. Also, signals using MSK modulation have a steeper out-of-bandsignal-energy roll-off, which reduces interference to adjacent channels.Unfortunately, the use of conventional frequency modulation (FM)discriminators in a typical MSK receiver creates a nonlinearity beforethe spread-spectrum codeword digital correlators. CDMA operation with anMSK receiver using an FM discriminator is therefore not desirable.

SUMMARY OF THE INVENTION

A general object of the invention is an MSK receiver which can receivespread-spectrum signals.

Another object of the invention is an economical approach to receivingspread-spectrum signals.

According to the present invention, as embodied and broadly describedherein, an MSK receiver and method is provided for receivingspread-spectrum signals. The method comprises the steps of generating anin-phase-component signal and a quadrature-phase-component signal fromthe received-spread-spectrum signal; processing the in-phase-componentsignal using sin_(doub) S(n,C) to generate a first processed signal, andusing cos_(doub) S(n,C) to generate a third processed signal; processingthe quadrature-phase-component signal using sin_(doub) S(n,C) togenerate a second processed signal, and using cos_(doub) S(n,C) togenerate a fourth processed signal.

For noncoherent reception, the third processed signal is combined withthe second processed signal to generate a first combined signal, and thethird processed signal is combined with an inverse of the secondprocessed signal to generate a second combined signal. The firstprocessed signal is combined with the fourth processed signal togenerate a third combined signal, and an inverse of the first processedsignal is combined with the fourth processed signal to generate a fourthcombined signal. From the first combined signal, the second combinedsignal, the third combined signal and the fourth confined signal, themethod determines an estimate of the data contained in thereceived-spread-spectrum signal.

For differentially coherent reception, the method combines the thirdprocessed signal with an inverse of the second processed signal togenerate a first combined signal. The first processed signal is combinedwith the fourth processed signal to generate a second combined signal.An angle is determined from the first combined signal and the secondcombined signal. From the angle the method determines an estimate of thedata contained in the received-spread-spectrum signal.

For differentially coherent reception of special type of codewords, thethird processed signal and the fourth processed signal need not begenerated. Instead, the method combines the first processed signal witha delayed version of the second processed signal to generate a firstcombined signal, and combines a delayed version of the first processedsignal with the second processed signal to generate a second combinedsignal. An angle is determined from the first combined signal and thesecond combined signal. From the angle the method determines an estimateof the data contained in the received-spread-spectrum signal.

Additional objects and advantages of the invention are set forth in partin the description which follows, and in part are obvious from thedescription, or may be learned by practice of the invention. The objectsand advantages of the invention also may be realized and attained bymeans of the instrumentalities and combinations particularly pointed outin the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of the specification, illustrate preferred embodiments of theinvention, and together with the description serve to explain theprinciples of the invention.

FIG. 1 illustrates a model of a spread-spectrum CDMA system with MSKmodems;

FIG. 2 is a phase state diagram;

FIG. 3 is a block diagram of an MSK noncoherent average chip phasereceiver;

FIG. 4 is a block diagram of a differentially coherent spread-spectrumMSK receiver;

FIG. 5 is a phase tree of spread-spectrum MSK signals;

FIG. 6 illustrates an output of a first matched filter which is matchedto cos_(doub) S(n,C);

FIG. 7 illustrates an output of a second matched filter which is matchedto sin_(doub) S(n,C);

FIG. 8 is a block diagram of a differentially coherent spread-spectrumMSK receiver of special types of codewords;

FIG. 9 illustrates error rate curves for an average chip phase receiver;and

FIG. 10 illustrates error rate curves for a differentially coherentspread-spectrum MSK receiver.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Reference now is made in detail to the present preferred embodiments ofthe invention, examples of which are illustrated in the accompanyingdrawings, wherein like reference numerals indicate like elementsthroughout the several views.

A novel noncoherent MSK receiver structure is disclosed for receivingspread-spectrum MSK modulation. The MSK receiver structure allows CDMAoperation because the MSK receiver's front end to the output of thecorrelators is linear. The nonlinear operation due to noncoherentdemodulation follows the correlators.

The primary new implementation requirements for this type of receiverare analog-to-digital (A/D) samples into the correlators, four insteadof two sets of sample registers, and frequency stability comparable tothat for coherent binary phase-shift-keyed (BPSK) systems.

A set of orthogonal, codewords is presented. "Orthogonal" is used in thesense of zero interuser interference at the output of the receiver. Adifferentially coherent spread-spectrum MSK receiver also is presentedas well as minimum interuser interference conditions in a synchronouscode division multiple access (S-CDMA) environment with such receivers.

NONCOHERENT SPREAD-SPECTRUM MSK RECEIVER

This section presents the conditions for zero interuser interference,and represents the sub-optimal noncoherent spread-spectrum MSK receiverwith sufficiently simple structure. The set of orthogonal, in the senseof the zero interuser interference at the output of the receiver,codewords is presented. The design of a differentially coherentspread-spectrum MSK receiver also is presented as well as minimuminteruser interference conditions in S-CDMA with such receivers.

FIG. 1 illustratively shows the model of a synchronous CDMA system withspread-spectrum MSK modems. A plurality of MSK modulators 21, 22, 23receive data d₁. The outputs of the modulators are x₁ (d₁, C¹), x₂ (t,d₂, C²), . . . , x_(M) (t_(M), C^(M)). The outputs are sent over acommunications channel, and additive white gaussian noise (AWGN) 24 isadded 25 to the signals. The combined signal from the channel are r(t).

A plurality of blocks of receivers, 26, 28, 30 with each receiver havingthe maximum likelihood receiver, are coupled to a plurality of decisiondevices 27, 29, 31. Accordingly, the block of maximum likelihoodreceivers 26 would be coupled to decision device 27. A second linearblock of maximum likelihood receivers 28 would be coupled to decisiondevice 29. The M^(th) linear block of maximum likelihood receivers 30would be coupled to decision device 31.

The spread-spectrum MSK transmitter signal is a constant envelope signalthat depends on the whether the data bit "d" is +1 or -1. Assume thatfor each data bit "d" the N chip sequence into the MSK modulator isgiven by dC. That is, for a conventional "1" data bit, the chip sequenceinto the MSK modulator is C, corresponding to d=1, and for aconventional "0" data bit, corresponding to d=-1, the chip sequence intothe MSK modulator is -C. During the time interval when a single data bit"d" is being sent, the constant envelope MSK signal includes themodulation of the N chip sequence dC.

Referring to the model in FIG. 1, there are M-users, each of which areindependent. One of the M-users, say user i, sends a ±1 data bit d_(i)by means of spread-spectrum MSK modulation, encoding his informationbits d_(i) into C.sup.(i) if d_(i) =1 ("1") , and -C.sup.(i) if d_(i)=-1 ("0"). Sequence C.sup.(i) includes the symbols ##EQU1## which arecalled chips. The transmitted spread-spectrum MSK signal at the outputof the modulator is

    x.sub.i (t,d,C.sup.(i))=Acos {w.sub.o t+p(t, d.sub.i C.sup.(i))+φ.sub.i }                                                         (1)

where ##EQU2## during the time interval nT<t≦(n+1)T

The phase state is defined as ##EQU3## The phase φ_(i) is the unknownphase that is equally likely to be anywhere between 0° and 360°. If thissignal x_(i) (t,d_(i) C.sup.(i)) were distorted by Additive WhiteGaussian Noise (AWGN) n(t) then the maximum likelihood (ML) non-coherentreceiver at first calculates ##EQU4## for d=1 and d=-1, respectively,where

    y(t)=X.sub.i (t, d.sub.i C.sup.(i))+n(t)                   (4)

and then makes the decision:

Choose the data bit d_(i) to be "1" if and only if ##EQU5## Suchreceiver is assigned to each user of FIG. 1.

The signal at the input of each receiver is ##EQU6## where n(t)is AWGN.

The signal r(t) at the input of the i^(th) receiver, in addition to theAWGN, also contains the interference noise ##EQU7##

In order to avoid the interference noise influence on the estimation ofthe data bit d_(i), the interference noise is eliminated at the outputof linear block of the receiver before doing nonlinear operation.

Thus, due to linearity of the first blocks of the receivers, the zerointeruser interference conditions for the i^(th) user in a S-CDMA systemwith spread-spectrum MSK modulation (1) (2) are ##EQU8## where d=±1,k=1,M, k≠i In this model, bit and chip synchronization are assumed, butthe initial phases of the signals of the different users are arbitrary.Synchronization is assumed also for the receiver.

The conditions in equations 7(a) and 7(b) are simplified by using thesignal representation (1), (2), (2a) and well known trigonometricalrelationships. Assuming that the d=1, d_(k) =1 yields ##EQU9## Ignoringthe last term and the factor of 1/2 and using the cosine relationshipyields ##EQU10## Since the last equality holds for any φ_(k) then (8)leads to two conditions ##EQU11## Condition (9a) by using again a cosinerelationship leads to ##EQU12##

The value of each the above integrals can be expressed by the value ofcosS (n,C), sinS (n,C), cosS (n+1,C) and sinS (n+1,C) regardless of thevalue of c_(n). For example, consider the integral in (9c) for an eventime interval from nT to (n+1)T, with n being even, and S(n,C(k))=0 or180°. The integral can be simplified by using the following expressions,which are apparent from the phase state circle consideration of FIG. 2.##EQU13## By using these expressions, the integral in (9c) can becalculated and instead of (9c) one has ##EQU14## where ##EQU15## is theconstant value and here and everywhere cosS (n,C).tbd. cos (0,C)=1 sins(n,C).tbd. sin (0,C)=0 Analogously, the condition (9b) leads to##EQU16## is the constant value.

Condition b_(i).sup.(k) (1)=0 leads to the similar (10a),(10b)conditions, but condition a_(i).sup.(k) (-1)=0 leads to two newconditions ##EQU17## For deriving (10c) and (10d), use the relationships

    cosS(n,-C)=cosS(n,C)

    sinS(n,-C)=-sinS(n,C)

The first two conditions (10a), (10b) are the conditions oforthogonality of two arbitrary spread-spectrum MSK signalsx(t,C.sup.(i)) and x(t,C.sup.(k)). In particular, the signals of singleuser x(t,C.sup.(i)) and x(t,-C.sup.(i)) are orthogonal if and only if##EQU18## The condition (10) can be satisfied if and only if C.sup.(i)and C.sup.(k) are chosen with the following properties ##EQU19## orequivalently (12a), (12b), (12c), and (12d) can be written as ##EQU20##respectively. The terms Cos _(doub) S(n,C) and Sin _(doub) S(n,C) meanthat in the CosS (n,C) and SinS (n,C) the zero components are replacedby their following one's.

For example, ##EQU21## For the optimal non-coherent MSK spread-spectrumreceiver defined by (3), (4), and (5), the sufficient and necessary zerointeruser interference condition on used codewords is given by (12a),(12b), (12c), and (12d) or equivalently by (12e), (12f), (12g), and(12h).

Suboptimal spread-spectrum MSK non-coherent receiver structure forspecial type of codewords, i.e., orthogonal signals, will now bediscussed. The goal is to represent a suboptimal MSK non-coherentreceiver which has a simple structure and evaluate the possibilities ofthe suggested receiver in S-CDMA. Assume that the receiver calculatesthe following values: ##EQU22## Let's allow the transmitter to use onlysuch codewords C.sup.(i) for which ##EQU23##

This receiver, which is called the Average Chip Phase (ACP) receiver,allows the simple structure implementation of FIG. 3. For every n^(th)chip time, the information containing phase p(t,C(i)), see (2) and (2a),varies linearly on time from S(n,C) to S(n+1,C). The optimal receivercorrelates the received signal with the signal having a phase whichvaries linearly in the same manner from S(n,C) to S(n+1,C), see (3). Thesuboptimal ACP receiver correlates the received signal with the signalhaving a phase which is equal to the average value of the informationcarrying phase for every n^(th) chip time, namely to(S(n,C)+S(n+1,C))/2, see (13). This ACP receiver can be implemented asin FIG. 3. ##EQU24## Evaluating the value of ##EQU25## in the sum fortwo successive chips n and n+1, letting n be odd, then, referring to thephase state circle of FIG. 2, ##EQU26## Thus two successive chips in thematched filter (MF) coincide, therefore a matched content is Cos_(doub)S(n,C). Finally it follows that (13) can be realized as in FIG. 3.

When the MSK signal x(t), as defined by (1) and (2) and with -φ insteadof φ_(i) and ignoring index i, is passed to the input of this receiverthen the outputs of the matched filters at the end of the bit intervalare: ##EQU27## where ##EQU28## and d is a transmitted data bit.

The decision rule for this receiver is the same rule (5) as for theoptimal receiver.

Since the best performance for the non-coherent receiver is achieved byusing orthogonal signals, the transmitter can be allowed to use onlysuch codewords C.sup.(i) for which x(t,C.sup.(i)) and x(t,-C.sup.(i))are orthogonal,i.e., for which the condition (11) holds ##EQU29## orequivalently ##EQU30##

The limitation (15) on the used signal with this receiver provides zerofor ##EQU31## are maximal and vice versa, for the noiseless case. Ifcodeword C.sup.(i) satisfied the limitation (15) then ##EQU32## Fortransmitted data D=1, see (14).

The ACP receiver can be shown to be suboptimal for orthogonal signals(15) by comparing this receiver with the optimal receiver defined by(3), (4), and (5). If the signal were introduced at the input of thereceiver as y(t)=x(t,dC)+n(t), where n(t) is an AWGN signal, then bycomparing (3a) and (3b) with (13a) and (13b) it can be seen that thenoise at the outputs of both receivers has the same characteristics, butthe MSK modulated signal x(t,dC) at the input of the ACP receiver has anamplitude α times larger than the MSK modulated signal at the input ofthe optimal receiver to produce the same signal-to-noise ratio.

Factor α can be found as follows: ##EQU33## which corresponds to 0.9 dB.

The loss of 0.9 dB is obtained for the receiver which employs orthogonalsignals (15) because, in this case, if transmitted data d=1 and noisewere absent, a(-1)=b(-1)=0 for the ACP receiver, see (16), as well asfor the optimal receiver, see (7a). On the other hand, a(1) and b(1) forthe ACP receiver are 1.11 times smaller than a (1) and b (1) for theoptimal receiver, see (17), if the same signal were at the inputs ofboth receivers. Because noise behavior on the outputs of both receiversis the same, the ACP receiver provides the same error probability as theoptimal receiver if the signal at the input of the ACP receiver had anamplitude 1.11 times larger than the signal at the input of the optimalreceiver. Thus loss=20 log 1.11=0.9 dB

It is not difficult to check, see (14), where cos_(doub) S(n,dC),sin_(doub) S(n,dC) should be substituted by cos_(doub) S(n,dC.sup.(i)),sin_(doub) S(n, dC.sup.(i)) and cos_(doub) S(n,C) , sin_(doub) S(n,C) bycos_(doub) S(n,C.sup.(k)), sin_(doub) S(n,C.sup.(k)) that zero interuserinterference conditions for S-CDMA with a non-coherent MSK suboptimal(0.9 dB) receiver coincide with conditions (10) or (12) derived earlierfor the optimal receiver.

As shown in FIG. 3, an optimal non-coherent a receiver for demodulatinga received-spread-spectrum OQPSK signal y(t), as defined by equations 13and 5, is shown comprising first generating means, second generatingmeans, first processing means, second processing means, third processingmeans, fourth processing means, first inverting means, second invertingmeans, first combining means, second combining means, third combiningmeans, fourth combining means and deciding means. The first processingmeans is coupled to the first generating means. The second processingmeans is coupled to the second generating means. The third processingmeans is coupled to the first generating means. The fourth processingmeans is coupled to the second generating means. The first invertingmeans is coupled to the first processing means, and the second invertingmeans is coupled to the second processing means. The first combiningmeans is coupled to the first processing means and to the fourthprocessing means. The second combining means is coupled through thefirst inverting means to the first processing means, and to the fourthprocessing means. The third combining means is coupled to the secondprocessing means and to the third processing means. The fourth combiningmeans is coupled through the second inverting means to the secondprocessing means, and to the third processing means. The deciding meansis coupled to the first combining means, to the second combining means,to the third combining means, and to the fourth combining means.

The first generating means generates an in-phase-component signal fromthe received-spread-spectrum signal y(t). The second generating meansgenerates a quadrature-phase-component signal from thereceived-spread-spectrum signal y(t). The first processing meansprocesses the in-phase-component signal using sin_(doub) S(n,C) togenerate a first processed signal. The second processing means processesthe quadrature-phase-component signal using sin_(doub) S(n,C) togenerate a second processed signal. The third processing means processesthe in-phase-component signal using cos_(doub) S(n,C) to generate athird processed signal. The fourth processing means processes thequadrature-phase-component signal using cos_(doub) S(n,C) to generate afourth processed signal. The first inverting means inverts the firstprocessed signal to generate an inverse of the first processed signal.The second inverting means inverts the second processed signal togenerate a inverse of the second processed signal.

The first combining means combines the first processed signal with thefourth processed signal to generate a first combined signal. The secondcombining means combines the inverse of the first processed signal withthe fourth processed signal to generate a second combined signal. Thethird combining means combines the second processed signal with thethird processed signal to generate a third combined signal. The fourthcombining means combines an inverse of the second processed signal withthe third processed signal to generate a fourth combined signal. Thedeciding means decides or selects an estimate of the data of thereceived-spread-spectrum signal y(t), from the first processed signal,the second processed signal, the third processed signal or the fourthprocessed signal.

In the exemplary arrangement shown in FIG. 3, the first generating meansis illustrated, by way of example, as signal generator 41, mixer 42,lowpass filter 43, and integrate-and-dump circuit 44. The mixer 42 iscoupled between the input, the signal generator 41, and the lowpassfilter 43. The integrate-and-dump circuit 44 is coupled to the output ofthe lowpass filter 43. The first generating means alternatively may beimplemented with other types of correlators, a matched filter surfaceacoustic wave (SAW) device, or equivalent circuitry, is well known inthe art.

The second generating means is shown as signal generator 41, mixer 47,lowpass filter 48, and integrate-and-dump circuit 49. The mixer 47 iscoupled between the signal generator 41 the lowpass filter 48, and tothe input y(t). The integrate-and-dump circuit 49 is coupled to theoutput of the lowpass filter 48. The second generating means may beimplemented with other types of correlators, a matched filter, surfaceacoustic wave (SAW) device or equivalent circuitry, as is well known theart.

By way of example, the first processing means is illustrated as a firstmatched filter 46 having impulse function sin_(doub) S(n,C). The firstmatched filter is coupled to the output of the integrated-and-dumpcircuit 44. The first processing means alternatively may be implementedusing a SAW device, a correlator embodied as a mixer, filter and signalgenerator, or other circuitry. When using a correlator, the signalgenerator would generate a signal with sin_(doub) S(n,C).

The second processing means is illustrated as second matched filter 51having impulse function sin_(doub) S(n,C). The second matched filter 51is coupled to the output of the integrate-and-pump circuit 49. Thesecond processing means alternatively may be implemented as a SAWdevice, a correlator embodied as a mixer, signal generator and filter,or other circuitry. When using a correlator, the signal generator wouldgenerate a signal with sin_(doub) S(n,C).

The third processing means is illustrated with a third matched filter 45having impulse function cos_(doub) S(n,C). The third matched filter 45is coupled to the output of the integrate-and-dump circuit 44. The thirdprocessing means alternatively may be implemented as a SAW device, acorrelator, embodied as a mixer, filter and signal generator, or othercircuitry. When using a correlator, the signal generator would generatea signal with cos_(doub) S(n,C).

The fourth processing means is illustrated by fourth matched filter 50having impulse function cos_(doub) S(n,C). The fourth matched filter 50is coupled to the output of the integrate-and-dump circuit 49. Thefourth processing means alternatively may be implemented as a SAWdevice, a correlator, embodied as a mixer, filter and signal generator,or other circuitry. When using a correlator, the signal generator wouldgenerate a signal with cos_(doub) S(n,C).

The first inverting means may be an invertor, or merely an invertinginput to the second combining means. The second inverting means may bean invertor, or an inverting input to the fourth combining means. Thefirst combining means, the second combining means, the third combiningmeans and the fourth combining means are illustrated in FIG. 3 as firstcombiner 53, second combiner 54, third combiner 52, and fourth combiner55. The first inverting means is shown as an inverting input to thesecond combiner 54. The second inverting means is shown as an invertinginput to the fourth combiner 55. The first combiner 53 is coupled to theoutput of the first matched filter 46 and to the output of the fourthmatched filter 50. The second combiner 54 is coupled to the output ofthe fourth matched filter 50 and has an inverting input or invertorcoupled to the output of the first matched filter 46. The third combiner52 is coupled to the output of the third matched filter 45 and to theoutput of the second matched filter 51. The fourth combiner 55 iscoupled to the output of the third matched filter 45 and has aninverting input or invertor coupled to the output of the second matchedfilter 51. The outputs of the first combiner 53, the second combiner 54,the third combiner 52, and the fourth combiner 55 are coupled to thedecision device 56.

The generator 41 generates a cosω_(o) t signal and a sinω_(o) t signal.To obtain the in-phase-component signal, the mixer 42 mixes thereceived-spread-spectrum signal y(t) with cosω_(o) t, and the lowpassfilter 43 filters the output of the mixer 42. The integrate-and-dumpcircuit 44 samples the output of the lowpass filter 43. At the output ofthe integrate-and-dump circuit 44 is the in-phase-component signal ofthe received-spread-spectrum signal y(t).

To obtain the quadrature-phase-component signal, the mixer 47 mixes thereceived-spread-spectrum signal y(t) with sinω_(o) t, and the lowpassfilter 48 filters the output of the mixer 47. The integrate-and-dumpcircuit 49 samples the output of the lowpass filter 48. At the output ofthe integrate-and-dump circuit 49 is the quadrature-phase-componentsignal of the received-spread-spectrum signal y(t).

The frequency ω_(o) would be equal to the carrier frequency of thereceived-spread-spectrum signal y(t) if the subsequent processing orfiltering were at baseband. The frequency ω_(o) would be different fromthe carrier frequency of the received-spread-spectrum signal y(t) if theprocessing or filtering were done at a frequency other than the carrierfrequency of the received-spread-spectrum signal y(t), such as anintermediate frequency, if SAW device were used for the first processingmeans, the second processing means, the third processing means, and thefourth processing means.

The first matched filter 46 processes or filters the in-phase-componentsignal using impulse function sin_(doub) S(n,C) to generate the firstprocessed signal. The second matched filter 51 processes or filters thequadrature-phase-component signal using impulse function sin_(doub)S(n,C) to generate the second processed signal. The third matched filter45 processes or filters the in-phase-component signal using impulsefunction cos_(doub) S(n,C) to generate the third processed signal. Thefourth matched filter 50 processes or filters thequadrature-phase-component signal using an impulse function cos_(doub)S(n,C) to generate the fourth processed signal. The impulse functionssin_(doub) S(n,C) and cos_(doub) S(n,C) may be approximated for eachmatched filter to accomplish the same result.

The first combiner 53 combines the first processed signal with thefourth processed signal to generate the first combined signal. Thesecond combiner 54 combines the inverse of the first processed signalwith the fourth processed signal to generate the second combined signal.The third combiner 52 combines the second processed signal with thethird processed signal to generate the third combined signal. The fourthcombiner 55 combines the inverse of the second processed signal with thethird processed signal to generate the fourth combined signal.

The decision device 56 decides or selects the estimate data of thereceived-spread-spectrum signal y(t) from the first processed signal,the second processed signal, the third processed signal or the fourthprocessed signal. For the embodiment shown in FIG. 3, a maximumlikelihood decision scheme might be used.

As another special case, consider OQPSK. The OQPSK signal can bedescribed by (1), but where p(t,dC) is defined in another manner thenfor MSK (2). ##EQU34##

Such definition of p(t,dC) leads to a spread-spectrum OQPSK signal. Theoptimal receiver structure is (3) (5), where p(t,dC) is defined above,which coincides with (13). Thus an optimal OQPSK receiver can beimplemented as in FIG. 3. The orthogonality conditions remain the sameas for MSK signals. The bit error rate curve for orthogonal OQPSKsignals coincides with the theoretical curve shown in FIG. 9.

Thus the ACP non-coherent spread-spectrum MSK receiver of FIG. 3 issuboptimal (0.9 dB) and allows S-CDMA operation of FIG. 1 with the zerointeruser interference condition if each user employs an MSK spreadspectrum modulated signal with codewords C.sup.(i), i=1,M, satisfyingthe conditions (12) and (15).

There can be several methods for choosing C.sup.(i), i=1,M, withproperties (12), (15). For example, as non-zero components of cosS(n,C.sup.(i)) i=1,M the rows of a first half of a Hadamard matrix ofSylvester type can be chosen; as non-zero components of sinS(n,C.sup.(i)) i=1,M the rows of the second half of the Hadamard matrixof Sylvester type can be chosen: ##STR1## Corresponding codewords are##STR2## The number of users M is equal to N/4, in this case, where N isthe length of the codewords.

DIFFERENTIALLY COHERENT SPREAD-SPECTRUM MSK RECEIVER

The performance of a spread-spectrum MSK non-coherent receiver can beimproved in the model where on unknown phase of the transmitted signalvaries slowly from bit to bit. In this case a differentially coherentreceiver, which is based on the ACP receiver structure of FIG. 3 is usedwith changed decision block as shown in FIG. 4.

In the exemplary arrangement shown in FIG. 4, a receiver fordemodulating a received-spread-spectrum signal y(t) is shown comprisingfirst generating means, second generating means, first processing means,second processing means, third processing means, fourth processingmeans, inverting means, first combining means, second combining means,and deciding means. The first processing means is coupled to the firstgenerating means. The second processing means is coupled to the secondgenerating means. The third processing means is coupled to the firstgenerating means. The fourth processing means is coupled to the secondgenerating means. The inverting means is coupled to the secondprocessing means.

The first combining means is coupled to the first processing means andto the fourth processing means. The second combining means is coupledthrough the inverting means to the second processing means and to thefourth processing means. The deciding means is coupled to the firstcombining means and to the second combining means.

The first generating means generates an in-phase-component signal fromthe received-spread-spectrum signal y(t). The second generating meansgenerates a quadrature-phase-component signal from thereceived-spread-spectrum signal y(t). The first processing meansprocesses the in-phase-component signal using sin_(doub) S(n,C) togenerate a first processed signal. The second processing means processesthe quadrature-phase-component signal using sin_(doub) S(n,C) togenerate a second processed signal. The third processing means processesthe in-phase-component signal using cos_(doub) S(n,C) to generate athird processed signal. The fourth processing means processes thequadrature-phase-component signal using cos_(doub) S(n,C) to generate afourth processed signal. The inverting means inverts the secondprocessing signal to generate a inverse of the second processed signal.

The first combining means combines the second processed signal with thefourth processed signal to generate a first combined signal. The secondcombining means combines the inverse of the first processed signal withthe third processed signal to generate a second combined signal. Thedeciding means decides or selects from the first processed signal andthe second processed signal, an estimate of the data of thereceived-spread-spectrum signal y(t). The deciding means may determinean angle from an arctangent of the ratio of the first combined signaland second combined signal, and compare the magnitude of the angle to90°. The estimate of the data is determined from the comparison.

As illustratively shown in FIG. 4, the first generating means isillustrated, by way of example, as signal generator 41, mixer 42,lowpass filter 43, and integrate-and-dump circuit 44. The mixer 42 iscoupled between the input, the signal generator 41, and the lowpassfilter 43. The integrate-and-dump circuit 44 is coupled to the output ofthe lowpass filter 43. The first generating means alternatively may beimplemented with a matched filter or equivalent circuitry, as is wellknown in the art.

The second generating means is shown as signal generator 41, mixer 47,lowpass filter 48, and integrate-and-dump circuit 49. The mixer 47 iscoupled between the signal generator 41, the lowpass filter 48, and tothe input. The integrate-and-dump circuit 49 is coupled to the output ofthe lowpass filter 48. The second generating means may be implementedwith a matched filter, as is well known in the art.

By way of example, the first processing means is illustrated as a firstmatched filter 46 having impulse function sin_(doub) S(n,C). The firstmatched filter is coupled to the output of the integrate-and-dumpcircuit 44. The first processing means alternatively may be implementedusing a SAW device, a correlator embodied as a mixer, filter and signalgenerator, or other circuitry. The signal generator would generate asignal with sin_(doub) S(n,C).

The second processing means is illustrated as second matched filter 51having impulse function sin_(doub) S(n,C). The second matched filter 51is coupled to the output of the integrate-and-dump circuit 49. Thesecond processing means alternatively may be implemented as a SAWdevice, a correlator embodied as a mixer, signal generator and filter,or other circuitry. The signal generator would generate a signal withsin_(doub) S(n,C).

The third processing means is illustrated with a third matched filter 45having impulse function cos_(doub) S(n,C). The third matched filter 45is coupled to the output of the integrate-and-dump circuit 44. The thirdprocessing means alternatively may be implemented as a SAW device, acorrelator embodied as a mixer, filter and signal generator, or othercircuitry. The signal generator would generate a signal with cos_(doub)S(n,C).

The fourth processing means is illustrated by fourth matched filter 50having impulse function cos_(doub) S(n,C). The fourth matched filter 50is coupled to the output of the integrate-and-dump circuit 49. Thefourth processing means alternatively may be implemented as a SAWdevice, a correlator, embodied as a mixer, filter and signal generator,or other circuitry. The signal generator would generate a signal withcos_(doub) S(n,C).

The inverting means may be an invertor, or merely an inverting input tothe second combining means. The first combining means and the secondcombining means are illustrated as first combiner 58 and second combiner53. The first combiner 58 is coupled to the output of the second matchedfilter 46 and to the output of the third matched filter 45. The secondcombiner 53 is coupled to the output of the fourth matched filter 50 andhas an inverting input or invertor coupled to the output of the firstmatched filter 46. The outputs of the first combiner 58 and the secondcombiner 58, are coupled to the decision device 56.

The generator 41 generates a cosω_(o) t signal and a sinω_(o) t signal.To obtain the in-phase-component signal, the mixer 42 mixes thereceived-spread-spectrum signal y(t) with cosω_(o) t, and the lowpassfilter 43 filters the output of the mixer 42. The integrate-and-dumpcircuit 44 samples the output of the lowpass filter 43. At the output ofthe integrate-and-dump circuit is the in-phase-component signal of thereceived-spread-spectrum signal y(t).

To obtain the quadrature-phase-component signal, the mixer 47 mixes thereceived-spread-spectrum signal y(t) with sinω_(o) t, and the lowpassfilter 48 filters the output of the mixer 47. The integrate-and-dumpcircuit 49 samples the output of the lowpass filter 48. At the output ofthe integrate-and-dump circuit 49 is the quadrature-phase-componentsignal of the received-spread-spectrum signal y(t).

The first matched filter 46 processes or filters the in-phase-componentsignal using impulse function sin_(doub) S(n,C) to generate the firstprocessed signal. The second matched filter 51 processes or filters thequadrature-phase-component signal using impulse function sin_(doub)S(n,C) to generate the second processed signal. The third matched filter45 processes or filters the in-phase-component signal using impulsefunction cos_(doub) S(n,C) to generate the third processed signal. Thefourth matched filter 50 processes or filters thequadrature-phase-component signal using an impulse function cos_(doub)S(n,C) to generate the fourth processed signal. The impulse functionssin_(doub) S(n,C) and cos_(doub) S(n,C) may be approximated for eachmatched filter to accomplish the same result.

The first combiner 58 combines the second processed signal with thefourth processed signal to generate the first combined signal. Thesecond combiner 53 combines the inverse of the first processed signalwith the fourth processed signal to generate the second combined signal.

The decision device 56 decides or selects the estimate data of thereceived-spread-spectrum signal y(t) from the first processed signal,and the second processed signal. For the embodiment shown in FIG. 4, anangle is determined from the arctangent 61 of a ratio of the firstprocessed signal and the second processed signal. The magnitude of theangle is compared 62 to determine if the magnitude is greater or lessthan 90°. The estimate data are selected or determined from thiscomparison.

In the case of full phase uncertainty the best performance for thespread-spectrum MSK modem was achieved for orthogonal signals. In thecase of differentially coherent implementation, the best performancewould be expected for antipodal signals as the representation ofdifferentially encoded data bits "0" and "1". To keep the phasecontinuity uninterrupted at the transition from bit to bit, signalswhich are "almost" antipodal are used; "almost" antipodal means that thesignals used are antipodal in every chip duration excluding the firstone and the last one, as shown in the phase tree in FIG. 5. ##STR3##

The phase tree of FIG. 5 shows the phase difference between signalscorresponding to differentially encoded data bits "1" and "0" is 180°during every chip time except the first chip time and the last chiptime. This can be achieved if the first C₀ and the last C_(N-1) chipcomponent of C₁ and C₀ are opposite and the remaining components are thesame (18). It can be seen also that ##EQU35##

The differentially coherent receiver estimates the carrier phase φ_(k)after transmission of the k^(th) bit to compare it with estimation ofφ_(k-1) by processing the outputs of a(1), b(1) which are

    a.sub.k (1)=2δN cos φ.sub.k                      (20a)

    b.sub.k (1)=2δN sin φ.sub.k,

if d=1 is transmitted and

    a.sub.k (1)=-2δN cos φ.sub.k +4δ(cos φ.sub.k -sin φ.sub.k)                                              (20b)

    b.sub.k (1)=-2δN sin φ.sub.k +4δ(cos φ.sub.k +sin φ.sub.k)

if d=0 is transmitted as k^(th) bit, e.g., the noiseless case, where##EQU36## (see (14) and (16), where C and -C must be changed by C₁ andC₀ for differentially encoded data bits "1" and "0", respectively So,thedecision is as follows:

Choose the data bit d_(i) to be "0" if and only if |φk-φk-1|<90° andvice versa.

The performance of the differentially coherent spread-spectrum MSKreceiver of FIG. 4 with almost antipodal signals was investigated by asimulation model in which it was assumed that there was no transmittercarrier phase change from chip to chip within each bit, but attransition from the k^(th) bit to the k+1^(th) bit, this phase φ_(k) canchange its value from φ_(k) to φ_(k+1) in the manner that φ_(k+1) takesequally likely values in the phase region

    {φk-Δ;φk+Δ}where Δ=0° or 10° or 20°,                                               (21)

i.e., dealing with a first order Markov process, φ_(o) is equally likelyto be anywhere between 0° and 360°. The simulation results are presentedin a following section.

Signals x(t,C₁) and x(t,C₀) are not perfectly antipodal because of thefirst chips and last chips. The effect of the first chips and last chipscan be escaped if, in the receiver of FIG. 4, instead of MF1, MF2, MF3,MF4, the shortened matched filters of length N-2 excluding firstcos_(doub) (0,C), sin_(doub) (0,C) and last cos_(doub) (N,C) ,sin_(doub) (N,C) components of the matched filters are used. Theninstead of (20a) (20b), one has:

    a.sub.k (1)=2δ(N-2) cos φ.sub.k

    b.sub.k (1)=2φ(N-2) sin φ.sub.k,

if d=1 is transmitted and

    a.sub.k (1)=-2δ(N-2) cos φ.sub.k

    b.sub.k (1)=-2δ(N-2) sin φ.sub.k

if d=0 were transmitted as the k^(th) bit, e.g., the noiseless case,where ##EQU37##

In order to simplify the structure of the differentially coherent MSKspread-spectrum receiver of FIG. 4, consider only such codewords C forwhich non-zero components of cosS (n,C) and sins (n,C) coincide. Thencos_(doub) S(n,C) and sin_(doub) S(n,C) can be written as

    cos.sub.doub S(n,C)=1a.sub.1 a.sub.1 a.sub.2 a.sub.2 . . . a.sub.N-1 a.sub.N-1 1                                               (22)

    sin.sub.doub S(n,C)=a.sub.1 a.sub.1 a.sub.2 a.sub.2 a.sub.3 . . . a.sub.N-1 11

FIGS. 6 and 7 illustrate that the output of the third matched filter 45which is matched to cos_(doub) S(n,C) and this case can be obtained bypicking up the output of the first matched filter 46 (sin_(doub) S(n,C))at one chip time instance earlier. Some distortion is possible for thefirst and last chips, but as we have noted above, these two chips can beexcluded by using shortened matched filters.

In FIGS. 6 and 7, the mean row of both tables includes the value ofsamples at the integrator output. The upper row is a content of thefirst matched filter 46 and the lower row is a content of the thirdmatched filter 46. As shown, the matched filtering procedure in thefirst matched filter 46 and the third matched filter 45 differs by onechip shift and therefore the realization of a simplified differentiallycoherent spread-spectrum MSK receiver in the case when sin_(doub) S(n,C)and cos_(doub) S(n,C) coincide with an accuracy of one chip shift can beimplemented as shown in FIG. 8, where D denotes the one chip delayelement.

DIFFERENTIALLY COHERENT SPREAD-SPECTRUM SPECIAL CODEWORD MSK RECEIVER

FIG. 8 shows a differentially coherent spread-spectrum MSK receiver forspecial type of codewords. If in practice it is necessary to accumulatethe value of a(1) and b(1) in any window, then the delay elements can beeliminated. By eliminating the delay elements, the operation of addingand subtracting of MFI and MFII in FIG. 8 can also be eliminated, ascorresponding to just rotation on 45°, resulting in derivation of theusual differentially coherent receiver for DBPSK signals. It can be seenthat if codeword C had the structure (22), then at every even chip timethe mean value of the information carrying phase of the MSK signal wouldbe -φ+45° or -φ+45°+180°, which roughly corresponds to BPSK signals.

As shown in FIG. 8, a differentially coherent spread-spectrum MSKreceiver for demodulating a received-spread-spectrum signal y(t) isshown comprising first generating means, second generating means, firstprocessing means, second processing means, first delaying means, seconddelaying means, inverting means, first combining means, second combiningmeans, and deciding means. The first processing means is coupled to thefirst generating means. The second processing means is coupled to thesecond generating means. The first delaying means is coupled to thefirst processing means. The second delaying means is coupled to thesecond processing means. The inverting means is coupled to the secondprocessing means. The first combining means is coupled to the firstprocessing means and to the second delaying means. The second combiningmeans is coupled through the inverting means to the second processingmeans, and to the first delaying means. The deciding means is coupled tothe first combining means and to the second combining means.

The first generating means generates an in-phase-component signal fromthe received-spread-spectrum signal y(t). The second generating meansgenerates a quadrature-phase-component signal from thereceived-spread-spectrum signal y(t). The first processing meansprocesses the in-phase-component signal using sin_(doub) S(n,C) togenerate a first processed signal. The second processing means processesthe quadrature-phase-component signal using sin_(doub) S(n,C) togenerate a second processed signal. The inverting means inverts thesecond processing signal to generate a inverse of the second processedsignal.

The first combining means combines a delayed version of the firstprocessed signal with the inverse of the second processed signal togenerate a first combined signal. The second combining means combinesthe first processed signal with a delayed version of the secondprocessed signal to generate a second combined signal. The decidingmeans decides or selects an estimate of the data of thereceived-spread-spectrum signal y(t), from the first processed signaland the second processed signal.

Referring to FIG. 8, the first generating means is illustrated, by wayof example, as signal generator 41, mixer 42, lowpass filter 43, andintegrate-and-dump circuit 44. The mixer 42 is coupled between theinput, the signal generator 41, and the lowpass filter 43. Theintegrate-and-dump circuit 44 is coupled to the output of the lowpassfilter 43. The first generating means alternatively may be implementedwith a matched filter or equivalent circuitry, as is well known in theart.

The second generating means is shown as signal generator 41, mixer 47,lowpass filter 48, and integrate-and-dump circuit 49. The mixer 47 iscoupled between the signal generator 41, the lowpass filter 48, and tothe input. The integrate-and-dump circuit 49 is coupled to the output ofthe lowpass filter 48. The second generating means may be implementedwith a matched filter, or equivalent circuit, as is well known in theart.

By way of example, the first processing means is illustrated as a firstmatched filter 45 having impulse function sin_(doub) S(n,C). The firstmatched filter is coupled to the output of the integrate-and-dumpcircuit 44. The first processing means alternatively may be implementedusing a SAW device, a correlator embodied as a mixer, filter and signalgenerator, or other circuitry. The signal generator would generate asignal with sin_(doub) S(n,C),

The second processing means is illustrated as second matched filter 50having impulse function sin_(doub) S(n,C). The second matched filter 50is coupled to the output of the integrate-and-dump circuit 49. Thesecond processing means alternatively may be implemented as a SAWdevice, a correlator, embodied as a mixer, signal generator and filter,or other circuitry. The signal generator would generate a signal withsin_(doub) S(n,C).

The first delaying means may be a delay device 66 which uses circuitry,or other means to accomplish delay. The second delaying means may be adelay device 67, which uses circuitry or other means to effect delay.

The inverting means may be an invertor, or merely an inverting input tothe second combining means. The first combining means, and the secondcombining means are illustrated as first combiner 63 and second combiner64. The first combiner 63 is coupled through the delay device 66 to theoutput of the first matched filter 45, and has an inverting input orinvertor coupled to the output of the second matched filter 50. Thesecond combiner 64 is coupled through the second delay device 67 to theoutput of the second matched filter 50 and to the output of the firstmatched filter 45. The outputs of the first combiner 63 and the secondcombiner 64 are coupled to the decision device 56.

The generator 41 generates a cosω_(o) t signal and a sinω_(o) t signal.To obtain the in-phase-component signal, the mixer 42 mixes thereceived-spread-spectrum signal y(t) with cosω_(o) t, and the lowpassfilter 43 filters the output of the mixer 42. The integrate-and-dumpcircuit 44 samples the output of the lowpass filter 43. At the output ofthe integrate-and-dump circuit is the in-phase-component signal of thereceived-spread-spectrum signal y(t).

To obtain the quadrature-phase-component signal, the mixer 47 mixes thereceived-spread-spectrum signal y(t) with sinω_(o) t, and the lowpassfilter 48 filters the output of the mixer 47. The integrate-and-dumpcircuit 49 samples the output of the lowpass filter 48. At the output ofthe integrate-and-dump circuit 49 is the quadrature-phase-componentsignal of the received-spread-spectrum signal y(t).

The first matched filter 46 processes or filters the in-phase-componentsignal using impulse function sin_(doub) S(n,C) to generate the firstprocessed signal. The second matched filter 51 processes or filters thequadrature-phase-component signal using impulse function sin_(doub)S(n,C) to generate the second processed signal. The impulse functionsin_(doub) S(n,C) may be approximated for each matched filter toaccomplish the same result.

The first combiner 63 combines a delayed version of the first processedsignal with the inverse of the second processed signal to generate thefirst combined signal. The second combiner 64 combines a delayed versionof the second processed signal with the first processed signal togenerate the second combined signal.

The decision device 56 decides or selects the estimate data of thereceived-spread-spectrum signal y(t) from the first processed signal andthe second processed signal. For the embodiment shown in FIG. 8, anangle is determined from the arctangent 61 of a ratio of the firstprocessed signal to the second processed signal. The magnitude of theangle is compared 62 to determine if the magnitude is greater or lessthan 90°. The estimate data are selected or determined from thiscomparison.

In S-CDMA in which the differentially coherent spread-spectrum MSK modemsystem signals assigned to each user are not perfectly antipodal, CDMAoperation with zero interuser interference is virtually impossible, butinterference noise can be reduced to a sufficiently insignificant levelsmall in comparison with intended signal energy so that zero interuserinterference a_(i).sup.(k) (1)=0, b_(i).sup.(k) (1)=0 (see 7a, 7b onlywith d=1) can be derived for a differentially coherent receiver withshortened matched filter by excluding the first and the last chips ofthe matched filter. The minimum interuser interference conditions, withusual matched filters, or the zero interuser interference conditions,with a shortened matched filter, can be written as follows (see (10a)(10b) or (14)): ##EQU38##

Recall that in an S-CDMA system with a non-coherent spread-spectrum MSKmodem, each user was assigned orthogonal signals for data "1" and "0".In an S-CDMA system with a differentially coherent spread-spectrum MSKmodem, these two orthogonal signals can be assigned to two differentusers. Therefore the number of orthogonal users can be doubled. Thenon-coherent receiver in FIG. 3 can serve two users, each of whom areemploying almost antipodal signals C₁.sup.(i), C₂.sup.(j) andC₁.sup.(j), C₂.sup.(j) for which cosS (n, C₁.sup.(i))=cosS (n,C.sup.(j)) sinS (n, C.sup.(i))=-sinS (n, C₁.sup.(j)). In this case datadetection of one user can be implemented by using a(1) b(1) outputs andthe data detection of the second user can be implemented by using a(-1)b(-1) outputs of the receiver shown in FIG. 3 to calculate the phase φvalue.

If the users employ codewords with properties (22) and a correspondingdifferentially coherent receiver has the structure shown in FIG. 8, thenthe minimum interuser interference conditions are (see (23a), (23b) with(22)): ##EQU39##

COMPUTER SIMULATION RESULTS NON-COHERENT SPREAD-SPECTRUM MSK ACPRECEIVER

In this section the performance analysis of the non-coherentspread-spectrum MSK receiver and error-rate curves are given. Theperformance measurement of the MSK receiver under AWGN was implementedby computer simulation using Monte-Carlo techniques. To simulate theeffect of channel noise, the independent identically distributedGaussian variables with zero mean and variance VAR were added tonoise-free integrator or lowpass filter LPF outputs at sampling instancein in-phase and quadrature arms, see FIG.3. At the receiver front-endthe data bit "0" is represented by spread-spectrum MSK signal x(t,C) andthe data bit "1" is represented by x(t,-C) (1), where 64-chip codewordC, to provide the orthogonality of x(t,C) and x(t,-C), was chosen inaccordance with limitation (15): ##EQU40## When the samples were takenafter the integrator to transfer the BER vs. VAR to BER vs. E_(b)/N_(o), the following relationships were used: ##EQU41## where T is achip duration, A is the amplitude of the MSK signal and N is the numberof chips. ##EQU42## where E{.} denotes math expectation and N_(o) is theone-sided spectral density of white noise.

From these relationships it follows that E_(b) /N_(o) =80/VAR, becausein the simulation N=64, T=π/2, A=2. When samples were taken after thelow pass filter and without an integrator, then the E_(b) /N_(o)=NWT/VAR, where W is an equivalent noise bandwidth of the low passfilter. The low pass filter was not simulated, ignoring its effect onthe baseband noise-free signal, but it was assumed that because of thegood spectral properties of the MSK signal, the approximation W=1.25/Tis valid for two samples per chip time, and W=2/T for four samples perchip time. As a result of computer simulation, the following performancecurves are plotted in FIG. 9.

As used in FIG. 9, "theoretical curve" illustrates the performance ofthe optimum non-coherent receiver (BER=0.5exp (-0.5Eb/No) . The "ACP"curve illustrates the performance of the ACP receiver. As seen, there isa degradation of about 1 dB compared to the optimum receiver.Synchronous 3-bit and 8-bit samples with AGC, give practically the sameresult as the ACP receiver.

The "3 bit async" curve illustrates the performance when 3-bit samplesof integrator output were taken asynchronously within T/2. There isdegradation of about 0.8 dB compared to the ACP receiver.

The "3 bit 2 samples" curve illustrates the performance of the receiverwith asynchronous 3-bit samples sampled two times during the chip timejust after the low pass filter. There is degradation of about 1 dBcompared to the ACP receiver.

The "1 bit sync" curve illustrates the performance when 1-bit samples ofintegrator output are taken synchronously at the end of every chip time.There is degradation about 2 dB compared to the ACP receiver. The "1 bitasync" curve illustrates the performance when 1-bit samples ofintegrator output are taken asynchronously within T/2. There isdegradation of about 3 dB compared to the ACP receiver.

The "1 bit 2 samples" curve illustrates the performance of the receiverwith asynchronous 1-bit samples sampled two times during the chip timejust after the low pass filter. There is degradation of about 3.5 dBcompared to the ACP receiver.

DIFFERENTIALLY COHERENT SPREAD-SPECTRUM MSK ACP RECEIVER

Performance measurement of the differentially coherent MSK receiver,shown in FIG. 4, under AWGN was implemented by computer simulation, inthe same manner as was the non-coherent MSK receiver. As the data bitrepresentation, the antipodal spread-spectrum MSK signal has been used((19),N=64). As a result of computer simulation, the following curvesare plotted in FIG. 10.

As used in FIG. 10, "theoretical curve" illustrates the performance ofdifferentially coherent PSK signals (BER=0.5 exp(-E_(b) /N_(o)). The"Diff ACP(0)" curve illustrates the performance of the differentiallycoherent receiver when relative phase instability from bit to bitΔ=0(see (21)).

The "Diff ACP(10)" curve illustrates the performance of thedifferentially coherent receiver when relative phase instability frombit to bit Δ=10(see (21)).

The "Diff ACP(20)" curve illustrates the performance of thedifferentially coherent receiver when relative phase instability frombit to bit Δ=20(see (21)).

The "1 bit 2 samples" curve illustrates the performance of thedifferentially coherent receiver with asynchronous 1-bit samples sampledtwo times during the chip time just after the low pass filter.

The "1 bit integrator" curve illustrates the performance when 1-bitsamples of integrator output are taken synchronously at the end of everychip time.

The "3 bit 2 samples" curve illustrates the performance of thedifferentially coherent receiver with asynchronous 3-bit samples sampledtwo times during the chip time just after the low pass filter.

The "1 bit 4 samples" curve illustrates the performance of thedifferentially coherent receiver with asynchronous 1-bit samples sampledfour times during the chip time just after the low pass filtercoinciding with the "1 bit integrator" curve. It should be noted thatsynchronous 3-bit samples with AGC give practically the same result as"Diff ACP(0)","Diff ACP(10)","Diff ACP(20)" correspondingly. Note alsothat integrator output sampled asynchronously leads to about 1 dB loss.Comparing the curves plotted in FIG. 10 coherent with the curves plottedin FIG. 9 shows that the differentially spread-spectrum MSK receiver hasan energetic gain of 2.5-2.8 dB compared with the non-coherentspread-spectrum MSK ACP receiver shown in FIG. 4.

It will be apparent to those skilled in the art that variousmodifications can be made to the MSK spread-spectrum receiver of theinstant invention without departing from the scope or spirit of theinvention, and it is intended that the present invention covermodifications and variations of the MSK spread-spectrum receiverprovided they come within the scope of the appended claims and theirequivalents.

We claim:
 1. A method for demodulating a received-spread-spectrum signalusing a minimum-shift-keyed (MSK) receiver, comprising the stepsof:generating an in-phase-component signal from thereceived-spread-spectrum signal; generating a quadrature-phase-componentsignal from the received-spread-spectrum signal; processing thein-phase-component signal using sin_(doub) S(n,C) to generate a firstprocessed signal; processing the quadrature-phase-component signal usingsin_(doub) S(n,C) to generate a second processed signal; processing thein-phase-component signal using cos_(doub) S(n,C) to generate a thirdprocessed signal; processing the quadrature-phase-component signal usingcos_(doub) S(n,C) to generate a fourth processed signal; combining thefirst processed signal with the fourth processed signal to generate afirst combined signal; combining an inverse of the first processedsignal with the fourth processed signal to generate a second combinedsignal; combining the second processed signal with the third processedsignal to generate a third combined signal; combining an inverse of thesecond processed signal with the third processed signal to generate afourth combined signal; and deciding from the first combined signal, thesecond combined signal, the third combined signal and the fourthcombined signal, an estimate of data of the received-spread-spectrumsignal.
 2. A method for demodulating a received-spread-spectrum signalusing a minimum-shift-keyed (MSK) receiver, comprising the stepsof:generating an in-phase-component signal from thereceived-spread-spectrum signal; generating a quadrature-phase-componentsignal from the received-spread-spectrum signal; processing thein-phase-component signal using sin_(doub) S(n,C) to generate a firstprocessed signal; processing the quadrature-phase-component signal usingsin_(doub) S(n,C) to generate a second processed signal; processing thein-phase-component signal using cos_(doub) S(n,C) to generate a thirdprocessed signal; processing the quadrature-phase-component signal usingcos_(doub) S(n,C) to generate a fourth processed signal; combining thefirst processed signal with the fourth processed signal to generate afirst combined signal; combining an inverse of the second processedsignal with the third processed signal to generate a second combinedsignal; determining an angle from the first combined signal and thesecond combined signal; and deciding from the angle an estimate of datafrom the received-spread-spectrum signal.
 3. The method as set forth inclaim 1, or 2, wherein:the step of processing the in-phase-componentsignal using cos_(doub) S(n,C) includes the step of filtering thein-phase-component signal using an impulse function matched tocos_(doub) S(n,C); the step of processing the in-phase-component signalusing sin_(doub) S(n,C) includes the step of filtering thein-phase-component signal using an impulse function matched tosin_(doub) S(n,C); the step of processing the quadrature-phase-componentsignal using cos_(doub) S(n,C) includes the step of filtering thequadrature-phase-component signal using an impulse function matched tocos_(doub) S(n,C); and the step of processing thequadrature-phase-component signal using sin_(doub) S(n,C) includes thestep of filtering the quadrature-phase component signal using an impulsefunction matched to sin_(doub) S(n,C).
 4. The method as set forth inclaim 3, wherein the step of determining the angle includes the step ofgenerating an angle from an arctangent of the first combined signal andthe second combined signal.
 5. The method as set forth in claim 1 or 2,wherein:the step of processing the in-phase-component signal usingcos_(doub) S(n, C) includes the step of correlating thein-phase-component signal with a signal having cos_(doub) S(n,C); thestep of processing the in-phase-component signal using sin_(doub) S(n,C)includes the step of correlating the in-phase-component signal with asignal having sin_(doub) S(n,C); the step of processing thequadrature-phase-component signal using COS_(doub) S(n,C) includes thestep of correlating the quadrature-phase-component signal with a signalhaving cos_(doub) S(n,C); and the step of processing thequadrature-phase-component signal using sin_(doub) S(n, C) includes thestep of correlating the quadrature-phase component signal with a signalhaving sin_(doub) S(n,C).
 6. The method as set forth in claim 5, whereinthe step of determining the angle includes the step of generating anangle from an arctangent of the first combined signal and the secondcombined signal.
 7. A method for demodulating a received-spread-spectrumsignal using a minimum-shift-keyed (MSK) receiver, comprising the stepsof:generating an in-phase-component signal from thereceived-spread-spectrum signal; generating a quadrature-phase-componentsignal from the received-spread-spectrum signal; processing thein-phase-component signal using sin_(doub) S(n,C) to generate a firstprocessed signal; delaying the first processed signal to generate afirst delayed-processed signal; processing thequadrature-phase-component signal using sin_(doub) S(n,C) to generate asecond processed signal; delaying the second processed signal togenerate a second delayed-processed signal; combining the firstprocessed signal with the second delayed-processed signal to generate afirst combined signal; combining the second processed signal with aninverse of the first delayed-processed signal to generate a secondcombined signal; determining an angle from the first combined signal andthe second combined signal; and deciding from the angle an estimate ofdata from the received-spread-spectrum signal.
 8. The method as setforth in claim 7, wherein:the step of processing the in-phase-componentsignal using sin_(doub) S(n,C) includes the step of filtering thein-phase-component signal using an impulse function matched tosin_(doub) S(n,C); and the step of processing thequadrature-phase-component signal using sin_(doub) S(n,C) includes thestep of filtering the quadrature-phase component signal using an impulsefunction matched to sin_(doub) S(n,C).
 9. The method as set forth inclaim 8, wherein the step of determining the angle includes the step ofgenerating an angle from an arctangent of the first combined signal andthe second combined signal.
 10. The method as set forth in claim 7,wherein the step of determining the angle includes the step ofgenerating an angle from an arctangent of the first combined signal andthe second combined signal.
 11. The method as set forth in claim 7,wherein:the step of processing the in-phase-component signal usingsin_(doub) S(n,C) includes the step of correlating thein-phase-component signal using an impulse function matched tosin_(doub) S(n,C); and the step of processing thequadrature-phase-component signal using sin_(doub) S(n,C) includes thestep of correlating the quadrature-phase component signal using animpulse function matched to sin_(doub) S(n,C).
 12. The method as setforth in claim 11, wherein the step of determining the angle includesthe step of generating an angle from an arctangent of the first combinedsignal and the second combined signal.
 13. A receiver for demodulating areceived-spread-spectrum signal, comprising:first generating means forgenerating an in-phase-component signal from thereceived-spread-spectrum signal; second generating means for generatinga quadrature-phase-component signal from the received-spread-spectrumsignal; first processing means, coupled to said first generating means,for processing the in-phase-component signal using sin_(doub) S(n,C) togenerate a first processed signal; second processing means, coupled tosaid second generating means, for processing thequadrature-phase-component signal using sin_(doub) S(n,C) to generate asecond processed signal; third processing means, coupled to said firstgenerating means, for processing the in-phase-component signal usingcos_(doub) S(n,C) to generate a third processed signal; fourthprocessing means, coupled to said second generating means, forprocessing the quadrature-phase-component signal using cos_(doub) S(n,C)to generate a fourth processed signal; first inverting means coupled tosaid first processing means for inverting the first processed signal;second inverting means coupled to said second processing means forinverting the second processed signal; first combining means, coupled tosaid first processing means and to said fourth processing means, forcombining the first processed signal with the fourth processed signal togenerate a first combined signal; second combining means, coupledthrough said first inverting means to said first processing means and tosaid fourth processing means, for combining an inverse of the firstprocessed signal with the fourth processed signal to generate a secondcombined signal; third combining means, coupled to said secondprocessing means and to said third processing means, for combining thesecond processed signal with the third processed signal to generate athird combined signal; fourth combining means, coupled through saidsecond inverting means to said second processing means and to said thirdprocessing means, for combining an inverse of the second processedsignal with the third processed signal to generate a fourth combinedsignal; and deciding means, coupled to said first combining means, tosaid second combining means, to said third combining means and to saidfourth combining means, for deciding from the first processed signal,the second processed signal, the third processed signal and the fourthprocessed signal, an estimate of data of the received-spread-spectrumsignal.
 14. A receiver for demodulating a received-spread-spectrumsignal, comprising:first generating means for generating anin-phase-component signal from the received-spread-spectrum signal;second generating means for generating a quadrature-phase-componentsignal from the received-spread-spectrum signal; first processing means,coupled to said first generating means, for processing thein-phase-component signal using sin_(doub) S(n,C) to generate a firstprocessed signal; second processing means, coupled to said secondgenerating means, for processing the quadrature-phase-component signalusing sin_(doub) S(n,C) to generate a second processed signal; thirdprocessing means, coupled to said first generating means, for processingthe in-phase-component signal using cos_(doub) S(n,C) to generate athird processed signal; fourth processing means, coupled to said fourthgenerating means, for processing the quadrature-phase-component signalusing cos_(doub) S(n,C) to generate a fourth processed signal; invertingmeans, coupled to said second processing means, for inverting the secondprocessed signal; first combining means, coupled to said firstprocessing means and to said fourth processing means, for combining thefirst processed signal with the fourth processed signal to generate afirst combined signal; second combining means, coupled to said thirdprocessing means and through said inverting means to said fourthprocessing means, for combining the third processed signal with theinverse of the fourth processed signal to generate a second combinedsignal; angle means, coupled to said first combining means and to saidsecond combining means, for determining an angle from the first combinedsignal and the second combined signal; and estimate means, coupled tosaid angle means, for deciding from the angle an estimate of data fromthe received-spread-spectrum signal.
 15. The receiver as set forth inclaim 13 or 14, wherein:said first processing means includes a firstfilter for filtering the in-phase-component signal using an impulsefunction matched to cos_(doub) S(n,C); said second processing meansincludes a second filter for filtering the in-phase-component signalusing an impulse function matched to sin_(doub) S(n,C); said thirdprocessing means includes a third filter for filtering thequadrature-phase-component signal using an impulse function matched tocos_(doub) S(n,C); and said fourth processing means includes a fourthfilter for filtering the quadrature-phase component signal using animpulse function matched to sin_(doub) S(n,C).
 16. The receiver as setforth in claim 13 or 14, wherein:said first processing means includes afirst correlator for correlating the in-phase-component signal with asignal having cos_(doub) S(n,C); said second processing means includes asecond correlator for correlating the in-phase-component signal with asignal having sin_(doub) S(n,C); said third processing means includes athird correlator for correlating the quadrature-phase-component signalwith a signal having cos_(doub) S(n,C); and said fourth processing meansincludes a fourth correlator for correlating the quadrature-phasecomponent signal with a signal having sin_(doub) S(n,C).
 17. A receiverfor demodulating a received-spread-spectrum signal, comprising:firstgenerating means for generating an in-phase-component signal from thereceived-spread-spectrum signal; second generating means for generatinga quadrature-phase-component signal from the received-spread-spectrumsignal; first processing means, coupled to said first generating means,for processing the in-phase-component signal using sin_(doub) S(n,C) togenerate a first processed signal; first delaying means, coupled to saidfirst processing means, for delaying the first processed signal togenerate a delayed-first-processed signal; second processing means,coupled to said second generating means, for processing thequadrature-phase-component signal using sin_(doub) S(n,C) to generate asecond processed signal; second delaying means, coupled to said secondprocessing means, for delaying the second processed signal to generate adelayed-second-processed signal; first combining means, coupled to saidfirst processing means and to said second delaying means, for combiningthe first processed signal with the delayed-second-processed signal togenerate a first combined signal; second combining means, coupled tosaid second processing means and to said first delaying means, forcombining the second processed signal with the delayed-first-processedsignal to generate a second combined signal; angle means, coupled tosaid first combining means and to said second combining means, fordetermining an angle from the first combined signal and the secondcombined signal; and estimate means, coupled to said angle means, fordeciding from the angle an estimate of data from thereceived-spread-spectrum signal.
 18. The receiver as set forth in claim17, wherein:said first processing means includes a first filter forfiltering the in-phase-component signal using an impulse functionmatched to sin_(doub) S(n,C); and said second processing means includesa second filter for filtering the quadrature-phase component signalusing an impulse function matched to sin_(doub) S(n,C).
 19. The receiveras set forth in claim 17, wherein:said first processing means includes afirst correlator for correlating the in-phase-component signal with asignal having sin_(doub) S(n,C); said second processing means includes asecond correlator for correlating the quadrature-phase component signalwith a signal having sin_(doub) S(n,C).